The consumption of tungsten (in metric tons) in a country is given approximately by p(t) = 136t² + + 1,07 1t+14,910, where t is time in years and t = 0 corresponds to 2010. (A) Use the four-step process to find p'(t). (B) Find the annual consumption in 2021 and the instantaneous rate of change of consumption in 2021, and write a brief verbal interpretation of these results. (A) p'(t) = C

A 600 gallon tank is initially half full with pure water. A mixture containing a concentration of 1 grams/gallon of salt enters the tank at a rate of 3 gallons/minute, and the well-stirred mixtureleaves the tank at 2 gallons/minute. (a)  Write a function for the volume in the tank as a function of time?  (b) Write the model for the rate of change for the Amount, A(t), in the for A'(t)= rate in - rate out  (c) What is the initial condition?

The table shows the age-adjusted death rates per 100,000 citizens for heart disease in a certain country. Complete parts (a) and (b) below. (a) Find an exponential model of the form f(t)=yob' for these data, where t=0 corresponds to the year 2000.Use the first and last data points to find a function. 1(t)=¹ (Round to two decimal places as needed.) (b) Assuming the model remains accurate, estimate the death rate in 2019 and 2024. The death rate in 2019 will be (Round to one decimal place as needed.) people per 100,000 The death rate in 2024 will be (Round to one decimal place as needed.) people per 100,000. Year 2000 2002 2004 2006 2008 2010 2012 2014 Death Rate 257.4 239.4 215.0 211.9 185.6 178.9 171.8 166.0

Suppose that P, is invested in a savings account in which interest is compounded continuously at 5.7% per year. That is, the balance dp P grows at the rate given by P = .057P(t) dt a) Find the function P(t) that satisfies the equation. b) Suppose that $1500 is invested. What is the balance after 3 years? 12